Liothyronine in Combination With BIT Regimen for Medulloblastoma With or Without Minimal Residual Disease

Inclusion Criteria: 1. Phase 1 and Phase 2, Cohort 1: Participants must have histologically confirmed medulloblastoma that is relapsed/progressive following standard upfront therapy. Tissue confirmation of medulloblastoma diagnosis is required at diagnosis and not required at the time of relapse for entry into the study. 2. Phase 2, Cohort 2: Participants must have cerebrospinal fluid (CSF) with cell-free deoxyribonucleic acid (cf-DNA) + assessed in a Chemiluminescent immunoassay (CLIA)-certified or protocol-approved laboratory. After entry into the study, another CSF sample will be collected and analyzed centrally prior to initiation of protocol therapy to verify cf-DNA positivity. 3. Evidence of Disease: Phase 1 and Phase 2, Cohort 1: Participants may have either Measurable or Evaluable Disease Measurable Disease: Participants must have clear residual disease at the time of enrollment, defined as tumor that is measurable in two perpendicular dimensions on MRI Evaluable Disease: Diffuse leptomeningeal disease OR clear MRI evidence of disease that may not be measurable in two perpendicular dimensions. Phase 2, Cohort 2: For cf-DNA positive cohort: Participants are not required to have measurable or evaluable disease but must have cf-DNA positivity in a CLIA-certified or protocol-approved laboratory, as above. 4. Prior Therapy: Participants must have received standard upfront therapy for medulloblastoma (either with craniospinal radiation or high dose chemotherapy and autologous stem cell rescue. If other therapy utilized, must be discussed with study chairs prior to participation). Participants for Phase 1 and Phase 2 cohort 1 may have received further chemotherapy and/or radiation therapy beyond standard upfront therapy prior to trial enrollment. Participants within the Phase 2 cohort 1 must have experienced at least one, and at most, two relapses prior to study enrollment. 5. Age 1-25 years old. 6. Performance Score: Karnofsky ≥ 50 for participants \> 16 years of age and Lansky ≥ 50 for participants ≤16 years of age (See Appendix A). Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. 7. For those participants currently treated with levothyroxine (Synthroid) they must have stable dosing for a minimum of 3 months prior to enrollment. 8. Organ Function Requirements 1. Peripheral absolute neutrophil count (ANC) ≥ 1000/cubic millimeters (mm3) 2. Platelet count ≥ 75,000/microliter (uL) (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment). 3. A serum creatinine \< 1.5 institutional/reference range upper Limit normal (ULN) based on age and gender 4. Total bilirubin ≤ 3 x upper limit of normal (ULN); in presence of Gilbert's syndrome, total bilirubin ≤ 6 x ULN or direct bilirubin ≤ 3 x ULN * Alanine aminotransferase (ALT) ≤ 5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) ≤ 5 x ULN. 3.3.7.4 Adequate Neurologic Function Defined as: * Participants with seizure disorder may be enrolled if well controlled. Participants on non-enzyme inducing anticonvulsants may be excluded pending interaction(s) with study drug. 3.3.7.5 Adequate Cardiac Function Defined as: * Normal left ventricular systolic function on baseline transthoracic echocardiogram (TTE) * Normal left ventricular systolic function is defined as left ventricular ejection fraction (LVEF) \>55% or shortening fraction (SF) \>28%. AND * No clinically significant arrhythmia on baseline ECG (sinus arrhythmia, sinus tachycardia, sinus bradycardia, early repolarization and 1st degree atrioventricular block when partial response (PR) interval \< 300 millisecond (ms) are not considered clinically significant arrhythmias). * In addition, the following ECG findings are not considered clinically significant in the setting of a normal echocardiogram: * Left axis deviation * Left atrial enlargement * Right atrial enlargement * Possible left ventricular hypertrophy * Possible right ventricular hypertrophy * Non-specific T wave abnormality 3.3.7.6 For the Phase 1 cohort, normal adrenal axis function is required. For those participants in the Phase 2 cohort, must have controlled adrenal insufficiency \>3 months (no change in steroid replacement or stress dose plan for at least 3 months). * Normal adrenal axis function as defined as: * Morning (AM) cortisol \>11mcg/deciliter (dL) * If AM cortisol is \<11 microgram (mcg)/dL, cosyntropin stimulation test with rise to \>18 9. Endocrine conditions: Participants with diabetes insipidus, diabetes melitus, or being treated with levothyroxine, must have stable dosing and control for minimum of 3 months prior to enrollment 10. For Cohort 1 only: participants must have recovered from any surgical procedure before enrolling on this study (see below for examples of major, intermediate, and minor surgical procedures): 1. Participants with a major surgical procedure within 28 days prior to enrollment should be excluded. 2. Participants with an intermediate surgical procedure within 14 days prior to enrollment should be excluded. 3. For minor surgical procedures (including Broviac line or infusaport placement), participants should not receive the first planned dose of bevacizumab until the wound is healed and at least 7 days have elapsed. 4. There should be no anticipation of need for major surgical procedures during the course of the study. 11. The effects of L-T3 with chemotherapy on the developing human fetus are unknown. For this reason and because chemotherapy agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and 4 months after completion of L-T3 and chemotherapy administration. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. 12. Participants must be enroll on PNOC COMP if PNOC COMP is open to accrual at the enrolling institution. 13. A legal parent/guardian or participant must be able to understand, and willing to sign, a written informed consent and assent document, as appropriate. Exclusion Criteria: 1. For Cohort 1 only: participants who have previously been treated with BIT in combination. Treatment with individual bevacizumab, irinotecan or TMZ is not an exclusion criteria. 2. Participants who have had myelosuppressive chemotherapy within 3 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. (Participants receiving chemotherapy directly into the CSF at doses not expected to be myelosuppressive may have received therapy up to 7 days prior to enrollment). 3. Participants must be at least 7 days since the completion of therapy with a biologic or small molecule agent or non-myelosuppressive chemotherapy agent. For any agent with known adverse events that can occur beyond 7 days after administration, the period prior to enrollment must be beyond the time during which adverse events are known to occur. Such participants should also be discussed with study chairs. 4. Radiation: For participants on the Phase 1 and Phase 2 Cohort 1, the tumor designated as "measurable" for protocol purposes must not have received radiation within 6 weeks prior to study entry and focal radiation to areas of symptomatic metastatic disease must not be given within 14 days of study entry. If a new lesion occurs outside the radiation field, the participant is eligible to enroll at any time point from completion of radiation. For Cohort 2 participants, there is no required washout for radiation therapy. 5. Participants who are receiving any other investigational agents. 6. History of allergic reactions attributed to compounds of similar chemical or biologic composition to L-T3 or other agents used in study. 7. Participants receiving any medications or substances that are strong inhibitors or strong inducers of CYP450 enzymes are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the participant and/or legal parent or guardian will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering. 8. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection. 9. Women of childbearing potential must not be pregnant or breast-feeding. 10. Human immunodeficiency virus- (HIV) positive participants will be ineligible if HIV therapy regimen has not been stable for at least 4 weeks or there is intent to change the regimen within 8 weeks following enrollment, or if they are severely immunocompromised. 11. Diagnosis of Graves' Disease or other pre-existing hyperthyroid disease. 12. Participants with severe protein calorie malnutrition that in the opinion of the investigator may not tolerate protocol therapy. 13. Participants with previous or active clinical cardiovascular disease, including the history of heart failure, myocardial infarction, cardiomyopathy, or ventricular systolic dysfunction on TTE (LVEF \<55% or SF \<28%), clinically significant arrhythmia (including atrial fibrillation, atrial flutter, frequent ventricular ectopy), clinically significant peripheral vascular disease. 14. Participants with uncontrolled systemic hypertension (systolic blood pressure \> 95th percentile for age and height if participant is ≤ 17 years old) 15. Participants with uncontrolled diabetes mellitus (HbA1c \>8%) or uncontrolled diabetes insipidus